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Derived from
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20410465 GE450 - TOPOLOGIA ALGEBRICA in Computational Sciences LM-40 CODOGNI GIULIO
(syllabus)
Omology of topological spaces. Homotopy invariance, Mayer-Vietoris, excision, Kunneth formula. Examples and application. Vietoris-Rips and Chech complexes associated to a data set, persistent homology, application to topologicla data analysis.
According to time and to interests of the class, we will also cover some of the following topics.
CW-complexes, Morse functions, persistent homology of manifolds associated to a Morse function, spectral sequences associated to persistent homology. Leray-Serre spectral sequences. Application to topological data analysis.
Cohomology, Poincaré duality, differential forms, De Rahm cohomology.
(reference books)
A. Hatcher: Algebraic Topology
Edelsbrunner, Harer, Computational Topology
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Università Roma Tre